ISTOSTRAND'S    SCIEJSTOE    SERIES. 


r,o  <•/*. 


PRACTICAL  DESIGNING 


TAINING  WALLS. 


ARTHUR    JACOB,    A.  B., 

ASSOCIATE    OP  THE     INSTITUTE    OP    CIVIL     EXGI.NKERS  J     I.ATK    RX- 

I'.ci   riVK    KXtilN-NKK.    II.    M.    BOMBAY    HKItVIOK. 


NEW    YORK: 

D.    VAN   NOSTRAND,   PUBLISHER, 

2::  MI-RUAY  A\I>  27  WAKKEX  STREKT. 

I  S  7  :; . 


PRACTICAL  DESIGNING 


OP 


RETAINING  WALLS. 


AETHUE    JACOB,    A.  B., 

ASSOCIATE  OF  THE    INSTITUTE    o*  CIVIL    ENGINEERS  ;    LATE  K- 
KCUTIVE  ENGINEER,   H.    M.    BOMBAY  SEKVICK. 


NEW    YOEK: 
D.   VAN  NOSTBAND,  PUBLISHES, 

23  MURRAY  A.VD  27  WARKEN  STHEET. 
1873. 


PEACTICAL  DESIGNING 
o* 

RETAINING    WALLS.* 


INTRODUCTORY. 


In  designing  masonry  works  there  ia 
hardly  any  subject  that  presents  itself  more 
frequently  than  the  retaining  or  revet- 
ment wall ;  and  in  some  form  or  other  it  is 
found  to  enter  into  almost  every  design. 
To  the  military  engineer  no  less  than  to 
his  civil  brother  is  the  subject  one  of  im- 
portance and  interest,  forming  as  the  re- 
vetment wall  does,  for  the  most  part,  a 
component  element  in  works  of  defence. 
To  military  engineers  in  truth  is  due  some 
of  the  most  valuable  information  that 

*  Practical  Designing  of  Retaining  Walls,  by  Arthur  Jacob, 
A.  B. 


civil  engineers  possess  regarding  the  theory 
of  earth  pressure,  and  although  further 
considerations  are  involved  in  designing 
revetments  for  military  works  than  the 
mere  support  of  earthwork,  there  is  still  to 
be  derived  from  the  experiments  and  re- 
searches of  military  men  information  of 
much  value  to  civil  engineers.  The  sub- 
ject is  one  that  has  received  the  fullest  and 
most  able  treatment  at  the  hands  of  mathe- 
maticians, and  solutions  for  every  case  that 
could  possibly  occur  in  practice  are  to  be 
found  in  our  text-books.  But  the  mathe- 
matical investigations  of  this  and  many 
other  questions  of  common  occurrence  in 
practice,  unquestionably  valuable  as  they 
are,  in  determining  the  principle  involved, 
and  establishing  final  rules  applicable  to 
practice,  are,  it  is  believed,  but  rarely  re- 
sorted to  by  practical  engineers.  Even 
when  such  examples  have  to  be  dealt  with 
by  those  sufficiently  acquainted  with  the 
mathematical  mode  of  proceeding,  they  are 
generally  solved  without  hesitation  by  some 
empirical  rule,  derived  from  experience. 
Such  a  method  may,  and  doubtless  occa- 


eionally  does,  lead  to  accident  from  weak- 
ness, and  not  unfrequently  to  clumsy  waste 
of  material  and  consequent  expense.  But 
it  is  not  clear  that  less  of  failure  or  clumsi- 
ness would  result  if  every  retaining  wall 
were  calculated  with  mathematical  preci- 
sion, for  in  truth  the  data  involved  are  so 
variable  and  imperfect,  and  the  disturbing 
causes  are  of  such  a  character  as  to  neutral- 
ize to  a  great  extent  the  accuracy  of  the 
investigation.  With  certain  specific  data 
theoretical  accuracy  can  always  be  attained ; 
but  the  engineer  as  a  rule  knows  nothing 
with  absolute  certainty  either  of  the  weight 
of  the  earth  he  has  to  sustain  in  position, 
or  of  the  masonry  that  he  intends  to  adopt 
in  doing  so.  These  and  other  data  he 
must  assume  before  he  enters  on  his  calcu- 
lations ;  and  though  there  is  not  in  these, 
as  in  many  other  investigations,  any 
necessity  to  attempt  an  extreme  degree  of 
refinement,  which  would  be  inapplicable 
for  every-day  practice,  yet  there  can  be  no 
good  excuse  for  dealing  with  the  matter  by 
hap-hazard  and  guess-work. 

It  is   not  proposed  now  to  regard  with 


G 


more  than  a  cursory  glance  the  principles 
involved  in  determining  the  strength  of 
walls  to  support  earthwork.  Such  simple 
rules  will  be  given,  as  it  is  hoped  will 
serve — due  regard  being  had  to  the  pecu- 
liarities of  each  particular  case — to  guide 
the  less  experienced  in  designing  works 
of  this  class.  The  empirical  mode  of  deal- 
ing with  the  question  is  clumsy  and  un- 
scientific, whilst  the  formulae  usually  given 
are  so  complicated  as  to  render  their  appli- 
cation to  practice  out  of  the  question. 

SPECIFIC    CAUSES    OF    FAILURE. 

It  must  not  be  presumed  that  the  failure 
and  destruction  of  a  retaining  wall  is  neces- 
sarily due  to  the  wall  being  of  itself  in- 
sufficiently strong.  It  may  be  quite  heavy 
enough  to  resist  the  pressure  of  a  bank,  if 
due  regard  be  had  to  the  mode  of  forming 
the  earthwork,  and  to  drainage ;  but  if 
these  points  be  not  fairly  considered  and 
observed  at  first,  a  retaining  wall  of  quite 
sufficient  thickness  will  probably  give  way 
sooner  or  later.  As  much  care  should  in 
fact  be  devoted  to  the  method  of  backing 


up  and  draining  a  wall,  as  to  the  calcula- 
tion of  its  section  ;  for  indeed  if  these  mat- 
ters be  disregarded,  no  retaining  wall,  pro- 
perly so  called,  can  be  implicitly  relied 
upon  to  stand.  With  the  exception  of  one 
particular  case,  which  will  be  noticed  here- 
after, walls  are  designed  on  the  assump- 
tion that  they  are  to  support  a  dry 
material — or  one,  at  any  rate,  not  per- 
meated by  water — and  that  the  material  is 
to  be  deposited  in  such  a  manner  as  to 
have  no  predisposition  to  slide  against  the 
wall.  It  is,  of  course,  also  presumed  that 
the  wall  shall  be  of  fair  workmanship  and 
materials,  and  where  these  points  cannot 
be  relied  upon,  as  is  sometimes  the  case, 
especially  in  foreign  works,  some  allow- 
ance should  be  made  in  the  dimensions  of 
the  wall.  It  has  not  unfrequently  hap- 
pened that  a  retaining  waU  will  have  stood 
for  a  considerable  number  of  years  without 
showing  any  appearance  of  yielding,  and 
yet  will  give  way  suddenly  and  completely, 
without  apparent  cause.  Such  failures  can 
generally  be  accounted  for  by  the  fact  of 
the  wall  not  being  designed  to  resist  a 


maximum  pressure,  and  never  having  been 
tried  fully  till  the  time  of  its  destruction. 
Much  apparent  anomaly  is  observed  in  the 
way  that  retaining  walls  are  found  to  fulfil 
the  purpose  for  which  they  are  designed : 
for  whilst  some  will  yield,  others  of  less 
dimensions  will  continue  to  stand;  such 
apparent  inconsistency  giving  occasion  for 
ingenious  theories,  most  of  them  entirely 
unsupported  by  fact  or  experience.  The 
truth  is,  that  imperfect  drainage,  defective 
foundations,  or  rotten  work  will  account  for 
almost  every  conceivable  case*  of  failure. 

FIRST    CASE HYDROSTATIC    PRESSURE. 

The  first  and  simplest  case  of  a  retaining 
wall  to  be  considered  is  that  in  which  the 
pressure  of  water  has  to  be  counteracted ; 
not  indeed  that  the  question  in  such  a  form 
belongs  strictly  to>the  subject  under  notice  ; 
but  it  nevertheless  becomes  absolutely  the 
method  of  determining  the  strength  of  walls 
for  certain  positions.  It  not  unfrequently 
happens,  as  in  some  hydraulic  works  or 
with  the  wing-walls  of  aqueducts,  that  the 
infiltration  from  beliind,  which  is  not  al- 


ways  avoidable,  may  produce  such  a  pres- 
sure as  no  retaining  wall  properly  so  called 
could  be  expected  to  bear.  With  this  view 
the  engineer's  limit  of  safety  will  be  attain- 
ed when  the  structure  is  designed  to  sus- 
tain the  full  hydrostatic  pressure.  The 
pressure  of  water  upon  any  plane  surface 
immersed  is  known  to  be  equal  to  the  area 
of  that  surface,  multiplied  by  the  depth  of 
its  centre  of  gravity  below  the  level  of  the 
water,  and  by  the  weight  of  a  unit  of  water. 
Generally  speaking  the  unit  adopted  in  cal- 
culation is  a  foot ;  and  the  unit  of  water 
being  taken  at  a  cubic  foot,  weighing  62.5 
Ibs.,  the  resulting  product,  from  the  multi- 
plication of  the  three  quantities,  will  give  the 
pressure  in  pounds  on  the  surface  immersed. 
Let  it  be  supposed  for  simplicity  that  water 
to  the  depth  of  10  ft.  has  to  be  sustained 
by  a  vertical  rectangular  wall.  It  is  usual 
to  take  but  1  ft.  length  of  the  wall  for  the 
calculation,  though  it  will  not  affect  the  re- 
sult whether  1  ft.  or  100  ft.  be  the  length 
assumed.  We  then  have  the  surface  under 
pressure  =  10  sq.  ft.,  the  depth  of  the 
centre  of  gravity  =  5  ft.,  and  the  weight  of 


10 


a  cubic  foot  of  water  =  62.5  Ibs. ;  the  pro- 
duct of  which  quantities  give  us  3,125  Ibs., 
the  pressure  on  1  ft.  length  of  the  wall.  But 
this  pressure  is  not  the  whole  of  the  force 
that  the  wall  has  to  resist ;  the  leverage 
that  it  exerts  must  also  be  taken  into  ac- 
count. In  the  example  under  considera- 
tion— namely,  that  of  a  vertical  plane,  with 
one  of  its  sides  coinciding  with  the  surface 
of  the  water,  as  in  Fig.  1. — the  whole  of 
the  pressure  is  so  distributed  as  to  be  equal 
to  a  single  force  acting  at  a  point  one-third 
of  the  depth  from  the  bottom.  Thus  the 
total  force  to  be  resisted  by  the  wall  is 
3,125  X  3.33  =  10,416,  which  is  the  mo- 
ment tending  to  overturn  the  wall. 

MOMENT    OF   RESISTANCE   TO    OVERTURNING. 

It  is  evident  that  a  certain  weight  of 
wall  must  be  opposed  to  this  overturning 
force ;  and  as  the  height  of  the  wall  and 
the  length  are  determined  quantities,  the 
thickness  alone  remains  for  adjustment. 
But  as  a  rectangular  wall  in  upsetting  is 
considered  to  turn  upon  a  single  point,  F, 
Fig.  1. — namely,  the  outer  line  of  the  foot 


11 


of  the  wall,  there  will  be  a  certain  amount 
of  leverage  to  assist  the  wall  in  resisting 
the  pressure  of  the  water.  This  leverage  is 
the  horizontal  distance  of  the  centre  of 
gravity  of  the  wall  from  the  turning  point 
F,  and  when  the  structure  is  rectangular 
and  vertical,  it  is  equal  to  half  the  thick- 
ness. The  amount  of  the  waWs  resistance 
will  then  be  equal  to  the  number  of  cubic 
feet  in  one  foot  of  its  length,  multiplied  by 
the  weight  of  a  single  cubic  foot  of  masonry, 
and  by  half  the  thickness  of  the  wall. 
Taking  w  =  the  weight  of  a  cubic  foot  of 
water  =  62.5  Ibs.,  wl  —  the  weight  of  a 
cubic  foot  of  masonry,  say  112  Ibs. ;  x  = 
thickness  of  the  wall,  and  h  =  the  height ; 
the  condition  of  simple  stability  will  be  ful- 
filled when 

to1  X  h  X  *  X  | -=  ic  X  h  X  -jj-  X  y      (1) 

wl  h  Xs      ic  h3 

~ =nr 

and  solving  for  x  we  get 


<» 


The  thickness  of  the  wall  =  4  ft.  4  in. 


12 


EXAMPLE. 

A  simple  example  has  been  selected  for 
illustration,  but  of  course  a  rectangular 
section  of  wall  would  not  be  found  gener- 
ally applicable  in  practice,  nor  would  it  be 
expedient  to  limit  the  dimensions  of  a  re- 
taining wall  of  whatever  kind  to  the  mini- 
mum that  would  sustain  the  pressure ; 
some  margin  of  safety  must  therefore  be 
allowed,  to  cover  inferior  work  and  materi- 
als. It  is  true  that  no  account  has  been 
taken  of  cohesion,  which,  if  the  wall  be 
founded  on  rock  or  concrete,  may  be  assum- 
ed to  add  to  its  stability  about  7,000  Ibs. 
for  every  square  foot  of  base.  In  addition 
to  this,  practice  seems  to  indicate  an  increase 
on  the  calculated  thickness,  and  in  the 
example  the  mean  width  might  be  aug- 
mented to  5  ft.,  the  stability  being  further 
increased  by  altering  the  section  from  a 
rectangle  to  a  battering  wall  with  offsets  at 
the  back. 

A  good  general  rule  for  the  dimensions 
of  a  wall  designed  to  support  water  or  earth 
in  a  semi-fluid  condition  will  be — 


13 

Top  breadth  =  0.3 
Middle  do.  «=  0.5 
Bottom  do.  «=  0.7 

The  height  being  represented  by  unity. 

Proceeding  to  the  consideration  of  walls 
for  the  support  of  dry  earth,  it  will  be  found 
that  the  question  is  one  that  will  in  general 
require  the  engineer  to  exercise  his  judg- 
ment, to  determine  what  angle  of  repose  he 
will  base  his  calculation  upon.  The  natural 
elopes  assumed  by  earths  of  different  tena- 
city are  so  various,  that  an  average  figure 
cannot  be  adopted  with  safety ;  the  calcula- 
tion of  pressure  from  earth,  in  fact,  depends 
essentially  on  this  point,  and  a  disregard  of 
it  will  lead  to  very  doubtful  results.  The 
following  are  a  few  of  the  slopes  assumed 
by  different  materials,  but  it  is  probable 
that  the  engineer's  judgment  will  be  of 
more  service  than  any  table  in  deciding  the 
angle  of  repose.  The  examination  of  a  dis- 
trict in  which  works  are  intended  to  be 
carried  out  will  always  suffice  to  satisfy  the 
designer  of  the  nature  of  the  material  that 
he  is  dealing  with,  and  may  enable  him  to 


14 


proportion  his  works  very  nearly  to  the  re- 
quirements of  safety  and  economy  : — 

Angle  of  repose.        Slope . 

Dry  sand,  clav  and  mixed  /From  37W          1.33  to  1* 

2.62  to  1 


earth \       to  21° 

Damp  clav 45* 

^t  clay' F™\% 

Shingles  and  gravel 4    ro™  QEO 

(From  45° 
I       to  14° 


Peat. 


1  to  1 
3.23  to  1 
4  to  1 
0.9  to  1 
1.43  to  1 
1  to  1 
4  to  1 


To  which  might  be  added  as  a  special  fea- 
ture London  clay ;  it  appears  under  the  in- 
fluence of  weather  to  be  exceedingly  un- 
stable, slipping  away  to  almost  any  angle 
of  repose. 

THEORY  OF  EA.RTH  PRESSURE. 

It  has  been  ascertained  by  M.  Prony  that 
when  a  vertical  wall  sustains  the  pressure 
of  a  bank  of  earth  the  top  of  which  is 
horizontal,  the  maximum  horizontal  pres- 
sure to  which  the  wall  can  be  subjected  will 
be  reached  when  the  plane  of  fracture  of 
the  earth  bisects  the  angle  that  would  be 
formed  were  the  earth  to  slope  from  the 

*  Rankine's  "Manual  of  Civil  Engineering." 


15 


foot  of  the  wall  backwards  at  the  natural 
inclination.  This  fact  is  somewhat  striking, 
for  it  would  appear  at  first  sight,  and  was 
for  long  assumed,  that  the  angle  of  fracture 
ought  to  coincide  with  the  natural  slope  of 
the  earth  ;  such  is,  however,  not  really  the 
case.  If  we  suppose  the  angle  made  be- 
tween the  sloping  plane  and  the  vertical  to 
be  bisected,  the  prism  of  earth  enclosed  be- 
tween the  bisecting  plane  and  the  wall  will 
represent  the  mass,  the  pressure  of  which 
has  to  be  resisted  ;  and  this  being  the  max- 
imum pressure  that  a  horizontal  topped 
bank  is  capable  of  exerting,  it  is  usually 
the  point  to  be  determined. 

Referring  to  Fig.  1,  the  principle  of 
earth  pressure  will  readily  be  understood. 
Supposing  the  plane  of  rupture  to  bisect 
the  angle  c — which  will  be  the  case  when 
the  pressure  is  a  maximum — the  prism  cut 
off  will  be  the  whole  weight  that  the  wall 
will  have  to  sustain.  Taking  this  prism 
for  a  single  unit  of  length  or  thickness,  the 
superficial  area  will  represent  the  cubio 
contents.  But  the  area  of  the  triangle, 
taking  7*  as  the  height  of  the  wall,  will  be 


16 


h*  tan.  £ o 
2 

c  being  the  angle  contained  between  the  na- 
tural slope  of  the  earth  and  the  back  of  the 
wall.  It  is  only  necessary  to  multiply  this 
value  by  w,  the  weight  of  a  cubic  foot  of  the 
bank,  to  get  the  total  weight  of  the  prism. 

FIG.  1. 


This  prism  of  earth  is  then  like  any  other 
body  resting  upon  an  inclined  plane ;  which 
in  this  case  is  the  plane  of  rupture.  It  is 
sustained  in  position  by  the  wall  on  one 
side  and  by  the  fixed  portion  of  the  bank 


17 


on  the  other ;  and  may  be  regarded  as  a 
solid  mass  of  material  without  motion 
amongst  its  parts.  The  line  K  M  repres- 
ents the  direction  of  the  force  of  gravity, 
and  the  lines  K  L  and  K  0  the  pressures 
exercised  against  the  wall,  and  the  force  of 
the  bank  respectively.  These  pressures 
produce  a  certain  amount  of  friction  against 
the  wall  and  the  bank,  but,  as  the  friction 
against  the  wall  does  not  materially  affect 
the  question,  the  friction  of  the  bank  alone 
is  considered,  and  taken  into  account  in 
arriving  at  the  following  formula  which 
applies  to  the  case  of  a  vertical  wall  sup- 
porting a  bank  with  a  horizontal-topped 
bank : — 

P=^|— tan.  •  Jc     .        .     (3) 

4  . 

Having  calculated  the  pressure  of  the  earth, 
the  next  step  will  be  to  determine  its  mo- 
ment to  overturn  the  wall,  and  this  can  be 
ascertained,  as  in  the  case  of  water,  by 
multiplying  the  pressure  by  one-third  of 
the  wall's  height.  This  having  been  de- 
termined the  next  consideration  will  be, 
what  weight  of  wall  will  suffice  to  sustain 


18 


it ;  and  the  method  of  arriving  at  this  is 
similar  for  the  most  part  to  that  adopted 
for  water.  Taking,  as  above,  the  moment 
of  the  wall  to  resist  the  pressure,  the  fol- 
lowing equation  will  represent  the  condi- 
tions of  stability : — 

w'  h  x*      ir  h*  h 

—  = tan.  2  i  c  -- 

4  it  o 

And  solving  for  x,  the  thickness  of  the  wall, 
we  have — 

/w  h*  tan.  •*  A  c 

X  ~~~    /  '--•--  (4} 

y  3  w' 

If  the  weight  of  a  cubic  foot  of  earth  be 
taken  equal  to  a  cubic  foot  of  the  wall,  the 
value  will  be —  

/&*  feB.'ifl 

*=V--3--'  '  (5) 
which  would  give  a  thickness  of  2.G9  ft.  for 
a  rectangular  wall  of  10  ft.  high  supporting 
a  bank  of  earth,  the  angle  of  repose  being 
taken  at  40  deg.  The  average  weight  of 
brickwork  and  ordinary  clay  will  generally 
be  nearly  the  same  ;  but  if  great  accuracy 
be  desired,  and  the  respective  weights  of 
the  materials  be  known,  the  general  formu- 
la No.  4  must  be  used. 


19 


The  following  table  gives  the  weight  per 
cubic  foot  in  pounds  avoirdupois  of  such  ma- 
terials as  come  under  our  consideration  in 
solving  questions  relative  to  retaining  walls : 

Weight  of  a 
cubic  foot 
in  pounds. 

Sand — damp 120 

Do.        dry 90 

Marl 100 

Clay 120 

Gravel 125 

Brick 130 

Brickwork 112 

Masonry 130 

Mortar 110 

PARTIAL   DETAINING  WALL. 

Having  so  far  considered  the  first  two 
cases,  namely,  those  of  a  wall  supporting  a 
horizontal-topped  bank  of  earth  in  a  semi- 
fluid condition,  and  also  in  a  state  of  com- 
parative dryness,  the  next  example  that 
suggests  itself  to  our  notice  for  examination 
is  that  of  a  partial  retaining  wall,  or  a  wall 
from  the  top  of  which  the  bank  slopes  away 
for  a  certain  height — called  the  surcharge 
— either  at  the  natural  slope  of  the  earth  or 
at  a  less  inclination.  Such  mode  of  con- 


20 


struction  is  of  very  common  occurrence, 
dwarf  walla  being  frequently  adopted  on 
railway  works  where  the  cuttings  or  em- 
bankments are  of  considerable  height,  and 
when  carefully  designed  are  found  to  effect 
a  saving  of  expense,  both  in  construction 
and  in  the  item  of  land.  In  cuttings  the 
walls  are  carried  up  to  such  a  height  as 
economy  dictates,  and  the  slope  is  then 
trimmed  back  at  the  proper  angle.  Simi- 
larly with  embankments,  the  walls  are  so 
disposed  as  to  cut  off  the  foot  of  the  slope. 
In  either  case  a  little  consideration  will  suf- 
fice to  show  whether  the  saving  of  earth 
and  land  area  will  cover  the  cost  of  the  re- 
taining walls.  In  military  works,  as  well 
as  civil,  the  partial  revetment  is  very  com- 
monly used,  being,  indeed,  a  component 
part  of  almost  every  system  of  fortification. 
The  first  particular  case  belonging  to  this 
class,  though  not  of  the  commonest  occur- 
rence in  civil  practice,  is  when  a  partial  re- 
taining wall  supports  a  bank,  the  face  of 
which  slopes  back  at  an  angle  less  than  the 
natural  slope  of  the  earth.  As  M.  Prony's 
rule,  that  the  plane  of  rupture  bisects  the 


21 


angle  between  the  natural  slope  of  the  earth 
and  the  back  of  the  wall,  only  holds  good 
when  the  surface  of  the  bank  is  at  right  an- 
gles to  the  plane  of  the  wall,  another  mode 
of  determining  the  angle  for  the  maximum 
pressure  must  be  resorted  to.  The  simple 
construction  given  in  the  note  enables  us  to 
arrive  at  the  maximum  pressure  for  a  wall 
at  any  given  batter,  with  the  surcharge 
above  sloping  at  any  inclination.  The 
equation  arrived  at  is  the  expression  for  the 
maximum  horizontal  pressure : 

p  _*-"&'       tan,  e  tan.  8  (c  -  ^)  g 

2     X      tan.  e  -  tan.  c 

the  angle  c  being  that  between  the  back  of 
the  wall  and  the  natural  slope ;  B  =  the  an- 
gle made  by  the  face  of  the  bank  with  the 
plane  of  the  wall ;  and  <f>  =  the  angle  be- 
tween the  plane  of  rupture  and  the  back  of 
the  wall.  The  value  for  c  —  <£  will  be  found 
in  the  note.  Taking,  for  example,  a  verti- 
cal wall  of  10  ft.  high,  supporting  a  bank 
that  slopes  back  at  an  inclination  of  20  deg. 
with  the  horizon,  the  natural  slope  being 
40  deg.,  the  value  of  tan.  (c.  —  0)  will  be 


22 


.4610;  inserting  this  value  and  working 
out  the  equation,  we  arrive  at  a  pressure  of 
2,100  Ibs.  against  the  back  of  the  wall. 

For  the  case  of  a  revetment  sustaining  a 
surcharge  the  centre  of  pressure  will  be,  as 
in  the  former  case,  at  one-third  of  the  height 
of  the  wall,  giving  a  leverage  of  3.33  feet. 
This  gives  2,100  Ibs.  X  8-33  =  6>993,  the 
moment  of  the  earth  tending  to  overturn 
the  revetment.  Equating  this  value  to  the 
moment  of  the  wall,  taking  the  cube  foot  of 
brickwork  at  112  Ibs.,  the  same  weight 
as  the  earth,  and  solving  for  x  the  thick- 
ness, we  find  it  to  be  3.53  ft. 

DEFINITE    SUECHABGE. 

The  next  case  to  be  considered  is  one  of 
much  mpre  frequent  occurrence  in  practice 
than  that  just  mentioned ;  it  is  a  partial  re- 
taining wall  supporting  a  surcharge  of  earth, 
sloping  away  at  the  natural  inclination, 
and  terminating  in  a  horizontal  plane  above. 
Cuttings  and  embankments  partly  supported 
by  masonry  works  furnish  familiar  ex- 
amples of  this,  which  is  denominated  the 
"  definite  surcharge."  The  most  convenient 


23 


method  of  determing  the  thickness  of  wall 
in  this  instance  will  be  to  consider,  first,  the 
conditions  of  stability  for  an  infinitely  long 
siope,  which,  however,  can  only_[have  a 

FIG.  2. 


theoretical  existence;  and  having  arrived 
at  the  thickness  of  wall  necessary  to  support 
such  a  bank,  a  simple  reduction  will  give 


the  thickness  required  when  the  length  of 
slope  is  limited. 

It  has  been  mentioned  that  when  a  verti- 
cal wall  sustains  a  bank  with  a  horizontal 
top,  the  plane  of  rupture  for  the  maximum 
pressure  is  found  to  bisect  the  angle  be- 
tween the  natural  slope  and  the  vertical. 
It  is  also  an  ascertained  fact,  that  as  the 
angle  of  the  surcharge  increases,  the  angle 
<f>,  or  that  between  the  plane  of  rupture  and 
the  back  of  the  wall,  also  increases ;  until 
the  face  of  the  bank  slopes  at  the  natural 
inclination  of  the  earth,  and  then  the  plane 
of  rupture  becomes  parallel  to  it.  From 
this  it  would  appear  that  when  the  slope  is 
infinitely  long — a  condition  that  could  not 
exist  in  practice— the  pressure  will  also  be 
infinitely  great ;  but  such  is  not  really  the 
case.  The  ratio  of  the  pressure  of  a  bank, 
whatever  its  inclination,  to  the  pressure 
exerted  by  an  embankment  level  with  the 
top  of  the  wall  can  never  exceed  4:1.  The 
formula,  then,  for  finding  the  maximum 
horizontal  pressure  exerted  by  an  infinitely 
long  slope  against  a  vertical  wall  will 
be— 


25 


(7) 


thp  notation  being  exactly  the  same  as  in 
the  other  cases  .  If  we  work  this  pressure 
out,  using  the  same  values  for  w,  h,  and  c, 
as  taken  above,  we  shall  find  P=3,281 
Ibs. 

Now  for  the  leverage  :  we  have,  as  in 
every  other  case,  simply  to  divide  the  height 
of  the  wall  by  3,  which  in  our  example 
gives  3.33  and  the  moment  to  overturn  the 
wall  =  3,281  X  3.33=10,925.  Proceeding 
in  the  same  manner  as  before,  the  width  of 
a  wall  of  brick  to  counterbalance  an  infi- 
nitely high  bank  sloping  at  the  natural 
inclination,  will  be  found  to  be  4.43  ft. 

When  the  surcharge  is  very  high  as 
compared  to  the  height  of  the  wall,  no  re- 
duction of  the  thickness  will  be  necessary, 
for  practically  the  slope  may  be  considered 
infinite  ;  but  when  the  bank  does  not  over- 
top the  wall  by  a  great  height  it  will  be 
well  to  apply  the  following  formula  to  as- 
certain the  corrected  thickness.  Let  A= 
height  of  wall=10  ft.,  /i'=height  of  sur- 
charge above  the  wall,  which  we  shall  take 


26 


at  20  ft.,  £=thickness  of  wall  to  support  a 
horizontal  bank,  as  found  in  the  first  case 
=2.69  ft.,  T=the  thickness  of  a  wall  for  a 
20  ft.  surcharge,  £x=thickness  for  indefinite 
slope  as  found=4.43.  Working  this  out 
the  thickness  is  found  to  be  408  ft. 


So  far  we  have  considered  the  cases  of 
more  usual  occurrence  in  practice,  namely 
those  in  which  the  back  of  the  wall  is  verti- 
cal or  stepped,  which  is  practically  the  same 
thing.  For  the  calculation  of  leaning  walls 
the  reader  is  referred  to  the  general  formu- 
las (A)  and  (B)  given  in  the  note  ;  from  the 
latter  formula  the  horizontal  resistance  of 
any  bank,  supported  by  a  wall  at  any  angle 
of  inclination,  can  be  ascertained,  and  the 
leverage  being  in  every  case  taken  at  one- 
third  of  the  height  of  the  wall,  there  will  be 
no  difficulty  in  designing  a  wall  of  such  a 
section  as  will  resist  the  pressure  of  the 
bank  effectually. 

The  point  to  be  kept  in  view  is  the  mo- 
ment of  the  wall,  and  this  must  be  made 


27 

to  exceed  the  maximum  overturning  force 
of  the  embankment.  It  will  not  suffice  to 
equalize  the  moment  of  the  earth's  force  to 
the  resistance  of  the  wall,  as  has  been  done 

FIG.  3. 


in  the  examples  above ;  a  certain  excess  of 
resistance  will  be  necessary,  and  this  can 
easily  be  attained  by  giving  the  wall  a 
batter,  or  else  sloping  it  back  so  as  to  throw 


28 


the  centre  of  gravity  of  the  mass  as  far 
back  as  possible,  in  a  horizontal  direction 
from  the  outer  line  of  the  foot  of  the  wall. 
The  line  of  the  centre  of  gravity  must  nott 
however,  be  allowed  to  fall  inside  the  base 
of  the  wall,  otherwise  the  stability  of  the 
structure  will  become  dependent  on  the 
support  of  the  bank,  and  will  have  a  ten- 
dency to  slide  away  from  its  position. 

It  has  been  stated,  and  taken  for  granted, 
that  banks  of  earth,  when  they  destroy  re- 
taining walls,  do  so  by  turning  them  over  ; 
this  is,  however,  not  invariably  the  case. 
It  has  occasionally  happened  that  walls 
have  been  moved  bodily  forward,  sliding  on 
their  base.  Such  an  occurrence  is  certainly 
accidental,  and  is  probably  the  result  of  the 
wall  having  been  founded  on  an  unstable 
material,  perhaps  on  an  inclined  bed  of 
moist  and  uncertain  soil.  Walls  have  also 
given  way  in  rare  instances  by  the  upper 
courses  of  the  structure  yielding  to  pressure, 
breaking  off  and  falling  over ;  a  contin- 
gency that  is  probably  due  to  the  upper  part 
of  the  bank  becoming  suddenly  charged 
with  water,  and  exercising  an  undue  pres- 


29 


sure  on  the  wall  before  there  is  time  for  the 
water  to  drain  away.  These  must  be  re- 
garded as  rare  contingencies,  arising  out  of 
some  defect  of  the  foundations,  or  backing ; 
and  cannot  affect  the  consideration  of  the 
wall's  stability  generally.  The  theory  of 
the  wall  being  turned  over  on  its  base  pro- 
vides for  the  greatest  trial  to  which  the 
structure  can  be  subjected,  or,  in  other  words, 
the  wall  would  as  a  general  rule  give  way 
under  a  much  less  pressure  by  falling  over, 
than  would  be  required  to  overcome  fric- 
tion, and  move  the  wall  forward  in  its  en- 
tire state  ;  if  therefore  the  structure  is  con- 
sidered as  having  to  withstand  the  over- 
turning force,  it  will  always  be  strong 
enough  to  resist  being  pushed  forward. 

BETAINIlfG   WALL  WITH   CURVED    BATTEB. 

A  form  of  retaining  wall  commonly  met 
with  in  practice,  especially  in  brickwork 
structures,  is  that  with  a  curved  batter, 
stepped  in  offsets  at  the  back.  The  curve 
usually  adopted  is  the  arc  of  a  circle,  the 
radius  of  which  is  from  2^  to  3  times  the 
wail's  height ;  and  the  centre  of  the  curve 


30 


is  as  a  rule  in  the  same  horizontal  plane  as 
the  top  of  the  wall.  In  such  structures  the 
courses  are  made  to  radiate  from  the  centre, 
and  the  result  is  that  the  joints  of  the 
brickwork  at  the  back  are  thicker  than  is 
either  necessary  or  advisable.  When  the 
radius  of  curvature  is  large,  the  increase  of 
thickness  is  inconsiderable,  but  it  becomes 
decidedly  an  objection  when  the  curve  is  a 
short  one ;  for  the  thickness  of  the  wall  will 
not  become  reduced  in  the  same  proportion 
as  the  height  or  as  the  radius  of  curvature. 
The  dimensions  of  a  wall  of  this  kind  may 
be  determined  with  sufficient  accuracy,  by 
first  considering  it  as  a  leaning  wall  at  a 
given  slope,  and  using  the  general  formula 
(6),  and  in  this  manner  a  very  close  ap- 
proximation to  the  thickness  may  be  arrived 
at.  There  are,  it  is  true,  specific  formulae 
given  by  some  authors  for  determining  the 
thickness  of  curved  walls,  but  they  are  too 
complex  for  application  in  practice.  The 
effect  of  the  curvature  will  be  to  add  to  the 
wall's  stability  by  bringing  the  centre  of 
gravity  farther  in  towards  the  bank,  and 
this,  indeed,  is  the  only  advantage  that  the 


31 


curved  form  possesses ;  it  is  difficult  to  con- 
struct, and  consequently  expensive  ;  for  the 
saving  of  material,  if  any,  is  very  trifling1. 
In  architectural  effect  it  certainly  has  no- 
advantage  over  the  wall  with  a  straight 
batter,  for  the  simple  reason  that  it  does 
not  convey  the  same  idea  of  strength.  If 
the  curved  wall  is  supposed  to  derive  any 
additional  stability  from  its  curvature,  on 
the  principle  of  the  arch,  as  some  have 
fancied,  it  must  be  recollected  that  an  arch 
with  but  one  abutment  is  a  very  unstable 
kind  of  structure,  and  such  kind  is  simply 
what  the  curved  retaining  wall  is.  Quays 
and  river  walls  may,  indeed,  be  designed  of 
a  curved  form  with  advantage,  for  such  will 
allow  of  ships  coming  closer  to  the  brink, 
than  they  could  were  the  wall  a  straight 
one.  And  sea  walls,  also,  are  not  unfre- 
quently  built  of  a  curved  section  on  the  face, 
this  form  being  under  certain  circumstances 
better  adapted  than  a  straight  wall  to  resist 
the  force  of  waves. 

In  situations  where  a  retaining  wall  has 
but   one   purpose  to    fulfil — that   of   sup- 

uu.ij.jv  vi   uux  tJJ. J.L  io  uauctl     tU  giVt) 


32 


the  base  of  the  wall  a  certain  amount  of 
inclination  to  the  horizontal,  the  slope  be- 
ing perpendicular  to  the  batter  of  the  face  ; 
or  if  the  wall  have  a  curved  batter,  the 
plane  of  the  base  will  simply  radiate  from 
the  centre  of  curvature.  Such  mode  of 
construction  is  calculated  to  increase  the 
frictional  stability,  for  it  brings  the  thrust 
of  the  earth  from  behind  more  nearly  per- 
pendicular to  the  bearing  surface. 

COTJXTEEFOEIS. 

Counterforts  are  frequently  constructed 
at  the  back  of  retaining  walls,  and,  al- 
though generally  approved  of,  appear  to  be 
a  somewhat  doubtful  mode  of  distributing 
material.  Mr.  Hosking,  in  a  paper  read 
before  the  Institute  of  Civil  Engineers, 
deprecates  their  use  and,  with  some  reason, 
advocates  the  use  of  ribs  or  arches  from 
wall  to  wall.  These  ribs  seem  to  have  been 
suggested  by  the  cast-iron  beams  used  to 
support  the  falling  walls  on  the  London 
and  North  Western  Railway  between 
Euston  Station  and  Primrose  Hill.  Mr. 
Hosking  proposes  that  his  arches  of  brick 


33 


should  pass  completely  over  the  road,  and 
that  they  should  consist  on  plan  of  a  pair 
of  flat  arches  placed  back  to  back.  Such 
an  arrangement  would  doubtless  prove 
effective,  and  the  expediency  of  adopting  it 
would  evidently  be  determined  by  the  cost 
of  the  work  and  the  value  of  land  adjoin- 
ing— a  mode  of  construction  in  common 
use  in  metropolitan  works,  and  in  other 
situations  where  land  is  very  valuable,  is 
that  shown  in  Fig.  4.  It  consists  of  a  series 

FIG.  4. 


[PLAN.] 


of  buttresses  and  inverts,  the  convexity  of 
which  latter  is  opposed  to  the  thrust  of  the 
backing.  Such  a  distribution  of  material 
is  most  suitable  in  situations  where  the 
projection  of  the  buttresses  is  not  found 
inconvenient.  In  quay  and  river  walls  it 


•would  not  answer  of  course  to  have  any 
such  projection,  as  the  near  approach  of 
ships  and  boats  is  an  essential  considera- 
tion. 

The  distribution  of  the  material  in  the 
form  of  counterforts  is  attended  with  a 
slight  saving,  and  where  buttresses  would 
be  inadmissible  on  account  of  their  en- 
croaching on  the  roadway,  counterforts 
may  be  adopted.  They  have  at  least  one 
use,  that  they  oppose  more  friction  to  the 
•earth  than  a  plain  wall,  and,  being  easy  of 
construction,  are  productive  of  but  little 
additional  expense.  In  order  to  ascertain 
what  additional  mean  thickness  a  wall  de- 
rives from  the  counterforts,  it  is  only  neces- 
sary to  multiply  the  length  of  the  counter- 
fort by  its  mean  width,  and  divide  the 
product  by  the  distance  from  centre  to 
centre  of  two  counterforts.  The  form  and 
dimensions  of  counterforts  vary  with  cir- 
cumstances, the  narrow  and  deep  disposi- 
tion of  the  material  being  probably  the  best 
as  a  general  rule.  The  late  Lieutenant 
Hope,  of  the  Royal  Engineers,  conducted 
some  interesting  experiments  on  the  sta- 


35 


bility  of  retaining  walls  generally,  and  ar- 
rived at  the  conclusion  that  a  thin  wall, 
with  frequent  thin  counterforts,  was  the  best 
arrangement  of  the  material. 

Two  points  of  importance  relative  to  coun- 
terforts demand  particular  attention — the 
first,  that  they  should  be  built  simul- 
taneously with  the  wall ;  and  the  second, 
that  the  wall  should  be  well  bonded  into 
the  counterforts,  otherwise  they  detract  from 
the  wall's  strength,  instead  of  augmenting 
it.  It  is  evident  that  without  some  special 
system  of  bond,  counterforts  reducing  the 
thickness  of  the  wall,  as  they  are  generally 
understood  to  do,  must  prove  detrimental 
rather  than  advantageous  ;  but  if  plenty  of 
hoop  iron  be  used,  which  is  not  usually  the 
case,  counterforts  may  be  made  to  contribute 
in  a  very  considerable  degree  to  the  stability 
of  the  wall.  In  fact,  quite  as  much  as  but- 
tresses. 

HODE    OF   BACKING   AND  DEAINAGE. 

That  accidents  frequently  occur  from  due 
care  not  being  exercised  in  the  mode  of 
backing-up  retaining  walls  is  undoubted 


36 


•and  indeed  to  this  cause  alone  the  majority 
of  failures  is  attributable ;  not,  as  is  fre- 
quently supposed,  to  the  insufficient  section 
•of  the  wall.  The  drainage  of  masses  of 
Dearth  sustained  by  walls,  is  a  matter  that 
can  only  be  disregarded  with  risk  of  ill 
consequences.  It  is  a  difficult  thing  to  pre- 
sent surface  water  from  finding  its  way 
into  earth-work,  and  therefore  the  simplest 
method  of  dealing  with  it  will  be  to  provide 
•efficient  means  for  its  escape.  To  this  end 
holes  or  weepers  should  be  left  in  the  wall 
.at  different  levels,  to  relieve  it  from  pressure 
from  behind ;  and  in  order  to  admit  the 
-surface  water  to  these  points  of  escape,  it 
-will  be  advisable  to  back  up  the  wall  with 
•dry  stone,  quarry  shivers,  or  whatever  else 
*vvill  admit  the  free  passage  of  water.  If  a 
Avail  be  backed  up  in  this  way  by  a  rough 
:angular  material,  it  will  be  relieved  of  al- 
most all  pressure  from  the  earth.  Economy 
•will,  however,  generally  preclude  such  an 
•expedient  in  works  of  considerable  extent, 
•and  then  it  will  be  necessary  to  form  the 
embankment  with  great  care,  adopting  every 
precaution  to  prevent  the  tendency  of  the 


37 


earth  to  slip  in  the  direction  of  the  wall. 
It  will  be  evident  from  the  calculation  of 
the  pressure  exerted  by  earth,  that  the  less 
the  angle  of  repose  is,  the  greater  will  be 
the  pressure  on  the  wall ;  and,  as  a  matter 
of  course,  any  means  that  will  tend  to  in- 
crease the  angle  of  repose,  will  relieve  the 
wall  of  a  certain  amount  of  pressure.  Ef- 
fectual drainage  will  do  much  towards  this 
end  ;  but  the  mode  of  depositing  the  earth 
will  also  affect  the  angle  of  natural  slope  in 
a  considerable  degree.  The  same  earth 
under  different  treatment  will  assume  dif- 
ferent slopes ;  if  dry,  it  will  fall  when 
tipped — at  a  low  angle,  but  if  damped,  and 
well  rammed,  will  adapt  itself  to  a  much 
higher  one.  It  has  even  been  found  that  a 
bank  when  constructed  in  such  a  manner  has 
stood  for  a  considerable  time  perfectly  verti- 
cal. The  best  mode  of  backing  a  wall  up  with 
earth  will  then  be,  to  commence  depositing  at 
the  foot  of  the  wall,  and  to  lay  the  earth  in 
layers  inclining  against  the  wall,  as  shown 
by  the  dotted  lines  in  Fig.  3,  each  layer 
being  well  rammed  before  another  is  com- 
menced. This  will  not  only  consolidate  the 


earth,  and  prevent  any  shock  that  might 
occur  from  sudden  settlement,  but  will  in- 
crease the  angle  of  repose,  and  give  the 
earth  a  tendency  to  slip  away  from  the  wall, 
rather  than  towards  it. 

THE   LAND    TIE. 

An  expedient  for  securing  retaining  walls 
that  is  simple  and  not  expensive,  is  the  land 
tie ;  it  consists  of  an  iron  plate,  with  a  rod 
passing  through  its  centre,  the  plate  being 
placed  vertically  in  the  bank  behind  the 
wall,  and  the  end  of  the  rod  passed  through 
the  wall  and  secured.  The  holding  power 
will  depend  on  the  area  of  the  plate,  and 
the  depth  at  which  it  is  sunk  beneath  the 
surface.  But  it  is  evident  that,  in  order  to 
act  most  effectually,  land  ties  should  be  at- 
tached to  the  wall  at  the  height  of  the  centre 
of  pressure. 

NOTE    I. 

The  following  construction,  given  by 
Mr.  Neville  in  the  "  Transactions  of  the 
Institute  of  Civil  Engineers,  Ireland,"  vol. 
i.,  shows  the  method  of  determining  the 


39 


pressure  exerted  by  a  bank,  whatever  may 
be  its  inclination  : 

FIG.  5. 


Let  C  D  represent  the  wall;  D  E  the 
face  of  the  bank  sloping  at  any  angle ;  and 
C  H  the  line  of  natural  slope.  Draw  any 
line  perpendicular  to  the  line  C  H,  cutting 
the  line  of  the  wall  produced  at  A,  and  also 
a  line  drawn  parallel  to  the  face  slope  at 
0.  On  A  0  describe  a  semicircle.  From 


40 


O,  as  a  centre  with  the  radius  0  H,  de- 
scribe an  arc  cutting  A  0  in  I  :  draw  I  C. 
The  triangle  CDF  represents  the  maxi- 
mum to  be  resisted.  The  angle  d  =  6  —  c. 
The  complement  of  the  angle  of  repose 
=  p  ;  and  the  face  C  D  =  h 

tan.  (c—  $>)  =  (tan.  2  <5+tan.  c  tan.  <5)  i—  tan.  S.  (A) 

Putting  R  for  the  maximum  horizontal  resist- 
ance, and  w  for  the  weight  of  a  cubic 
unit  of  the  bank,  the  resistance  of  pressure 
will  be 

•R  —  v'  **  tan-  6  tan-  '  (c  —  ft)  ,,,. 

2          tan.  0-tan.  c. 

in  which  the  value  (c  —  0)  found  above 
must  be  substituted.  When  C  D  E  is  a 
right  angle  we  shall  have 


(C) 


the  equation  given  in  the  first  part  of  this 
article  ;  and  that  which  holds  good  when 
the  slope  of  the  bank  is  at  right  angles  to 
the  face  of  the  wall. 

The  following  tables  calculated  by  Mr. 
J.  H.  E.  Hart,  Executive  Engineer  of  the 


41 


Bombay  Department  of  Public  Works,  are, 
by  his  kind  permission,  appended  to  this 
pamphlet,  and  will  be  found  very  con- 
venient for  the  calculation  of  Retaining 
Walls. 

Knowing  the  angle  of  repose  of  the  earth 
to  be  supported,  and  the  relative  weights  of 
the  masonry  of  the  wall  and  of  the  earth 
per  cubic  unit,  a  simple  reference  to  the 
table  will  give  a  coefficient,  which  multi- 
plied by  the  height  will  give  the  requisite 
thickness.  For  example,  supposing  a  hori- 
zontal topped  bank  has  to  be  supported  by 
a  masonry  wall  of  10  ft.  high,  and  of  twice 
the  specific  gravity  of  the  earth,  the  angle 
of  repose  of  the  latter  being  35  deg. 
Under  the  fraction  |,  and  opposite  to  35 
deg.,  will  be  found  in  Table  A  the  fraction 
.212,  which  multiplied  by  10,  the  height  of 
the  wall,  gives  2.12  ft.,  the  required  mean 
thickness. 


42 


* 

H? 


rCS^i-ii-iOOCaCiCiaooOI^-t-*  CO  SO  £ 

3>  O  O  rH  t^-  OJ  t"—  CO  O  •**•  O  '^  rH  L^*  CO  O 
5O  5s)  5s!  ^*  ff^  ^  C^l  G^l  r^  rH  r^  i~i  r-t  rH  rH  H 

•^f*  <N  C^l  l?^  C-)  ^  C1)  C^l  2s)  —  i— I  r- 1  rH  rH  rH  r- 

•^  »C  O  -^  "^  CO  CO  <M  "T-l  T— •  rH  O  O  O  O  0< 

t-  rtH  QO  (M  co  o  rtH  GOS^r^rHirso^Oicr; 


12 


_;  . 


._  O  i-l  fN  CO  -f  O  !S  t^  00  T5  O  i-(  'M  CO  • 

O  co  co  »  co  cc  co  co  co  cc  co  •*  i<  •*  •*  > 


43 


co:ocacocococo545i5iH'MS<i(NCN& 

cococoeocococortcccccocococb-r.  S 

ri  T-I  r-i  o  o  5;  sv  x  x  •  £.  i  -  -~  -b  >o  '?5  TH 
cocoJi'M^Hi-iosSjcrjxooi^i^iom 

o  I-H  jo  TH  »  o  -c  ^  co  r^  i-t  i^  o  01  o  e» 
o ' •*  cs  co  oo  *a  r^ "  1-1  o  ao  TI  o  o»  7*  i*  ao 


<M 

H  . 


jS 


CO  CO  CO  CO  CO  CC  CO  tC  '1  CO 


44 


NOTE   II. 

The  following  graphic  method  for  de- 
termining the  pressure  of  earth  against 
a  retaining  wall,  we  take  from  "  Engineer- 

ing:" 

Referring  to  Fig.  1,  let  us  determine, 
first,  the  pressure  exerted  by  the  wedge, 
A,  B,  C,  the  angle,  B,  A,  E,  being  greater 
than  <£,  the  limited  angle  of  resistance  of 
the  wedge  against  A,  B,  which  is  also 
identical  with  the  natural  slope  of  the 
earth.  The  friction  against  the  back  of 
the  wall  is  neglected.  We  have  now  3 
forces  to  deal  with — namely,  the  weight 
of  the  triangle,  A,  B,  C,  acting  vertically 
through  its  centre  of  gravity,  and  there- 
fore passing  through  the  point  c,  where 
A,  c  =  ^  A,  B  ;  next,  the  resistance  of  the 
plane  A,  B,  the  direction  of  which  is  in- 
clined at  an  angle,  $,  to  the  normal  to  A, 
B ;  and,  lastly,  the  thrust  against  the  back 
of  the  wall  acting  horizontally  through 
c,  and  cutting  A,  C  in  a  point,  g,  where 
A  g  =1  A,  C. 


45 


Now,  since  the  weight  of  the  wedge,  A 
B  C,  is  proportional  to  0  B,  the  height  of 
the  wall  remaining  constant,  and  the  slope 
varying,  if  we  set  off  c  b  =  0  B,  and  com- 
plete the  triangle  of  forces,  a  b  will  rep- 
resent the  thrust  against  the  back  of  the 
wall. 

Let  us  now  observe  the  effect  produced 
by  altering  the  slope  A  B,  to  A  D. 

Construct  the  triangle  of  forces  d  e  f,  as 
before,  making  d  f=  C  D,  to  represent 

FIG.  1. 


the  weight  of  A  C  D.     The  angle,  e  d  /,  is 
now  greater  than  the  angle  a  c  b,  by  the 


46 


same  amount  that  we  have  increased  the 
slope  of  A  B  to  A  D  ;  that  is  to  say,  the 
angle  e  df=  a  c  b  -\-  angle  DAB. 

Also,  the  length  of  b  c  has  decreased  to 
fd  in  the  ratio  of  C  B  to  C  D. 

Supposing  now  we  divide  up  the  angle 
OAF  into  any  number  of  equal  angles  by 
the  radial  lines  At  A3  A3,  etc.  (see  Fig.  2), 
and  imagine  the  slope  of  A  B  to  be  altered 

FIG.  2. 


to  each  of  these  positions  successively,  we 
shall  then  for  each  alteration  have  a  new 
triangle  of  forces  ;  for  instance,  in  moving 
from  the  position  Az  to  A2  the  angle  b  A  p, 
of  the  triangle  of  forces  will  increase  to  c  A 
q  in  the  same  ratio  that  the  slope  of  the 


47 


plane  varies,  and  the  side  A  b  will  decrease 
to  A  c  in  the  same  ratio  that  C^  decreases 
toC,. 

We  are  thus  enabled  to  make  a  diagram 
illustrating  the  successive  changes  by  a 
curve,  e  d  c  b,  A.  b,  A.  c,  A.  d,  etc.,  being 
respectively  equal  to  C1}  C2,  C3,  etc.  The 
lines  b  p,  c  q,  d  r,  e  s,  and  c  drawn  at  right 
angles  to  A  b,  A.  c,  A  d,  etc.,  will  now  re- 
present the  thrusts  against  the  back  of  the 
wall  at  the  different  slopes,  and  it  will  be 
observed  on  examining  the  diagram  that 
the  position  which  gives  the  greatest  mag- 
nitude to  the  line  representing  the  thrust  is 
the  slope  A4,  which  bisects  the  angle  C 
AF. 


*»*  Any  book  in  this  Catalogue  sent  free  &j/  matt  on 
receipt  of  price. 


PUBLISHED   BY 

D.  VAN   NOSTRAND, 

23  MURRAY  STREET  AND  27  WARREN   STREET, 
NEW  YORK. 


FRANCIS.  Lowell  Hydraulic  Experiments,  being  a 
selection  from  Experiments  on  Hydraulic  Motors,  on 
the  Flow  of  Water  over  Weirs,  in  Open  Canals  of 
Uniform  Rectangular  Section,  and  through  submerg- 
ed Orifices  and  diverging  Tubes.  Made  at  Lowell, 
Massachusetts.  By  James  B.  Francis,  C.  E.  2<1 
edition,  revised  and  enlarged,  with  many  new  experi- 
ments, and  illustrated  with  twenty-three  copperplate 
engravings,  i  vol.  410,  cloth $15  o*- 

ROEBLING  (J.  A.)  Long  and  Short  Span  Railway 
Bridges.  By  John  A.  Roebling,  C.  E.  Illustrated 
with  large  copperplate  engravings  of  plans  and  views. 
Imperial  folio,  cloth 25  oo 

CLARKE  (T.  C.)  Description  of  the  Iron  Railway 
Bridge  over  the  Mississippi  River,  at  Quincy,  Illi- 
nois. Thomas  Curtis  Clarke,  Chief  Engineer. 
Illustrated  with  21  lithographed  plans,  i  vol.  ^to, 
cloth 7  50- 

TUNNER  (P.)  A  Treatise  on  Roll-Turning  for  the 
Manufacture  of  Iron.  By  Peter  Tunner.  Trans- 
lated and  adapted  by  John  B.  Pearse,  of  the  Penn- 


I).   VAN    NOSTBAND  S    rUBUCATIOXS. 

sylvania  Steel  Works,  with  numerous  engravings 
wood  cuts  and  folio  atlas  of  plates. $10  oo 

ISHERWOOD  (B.  F.)  Engineering  Precedents  for 
Steam  Machinery.  Arranged  in  the  n-.ost  practical 
and  useful  manner  for  Engineers.  By  B.  F.  Isher- 
wood,  Civil  Engineer,  U.  S.  Navy.  With  Illustra- 
tions. Two  volumes  in  one.  Svo,  cloth $2  50 

BAUERMAN.  Treatise  on  the  Metallurgy  of  Iron, 
containing  outlines  of  the  History  of  Iron  Manufac- 
ture, methods  of  Assay,  and  analysis  of  Iron  Ores, 
processes  of  manufacture  of  Iron  and  Steel,  etc.,  etc. 
By  H.  Bauerman.  First  American  edition.  Revised 
and  enlarged,  with  an  Appendix  on  the  Martin  Pro- 
cess for  making  Steel,  from  the  report  of  Abram  S. 
Hewitt.  Illustrated  with  numerous  wood  engravings. 
121110,  cloth 2  oo 

CAMPIN  on  the  Construction  of  Iron  Roofs.  By 

Francis  Campin.  Svo,  with  plates,  cloth 30* 

COLLINS.  The  Private  Book  of  Useful  Alloys  and 
Memoranda  for  Goldsmiths,  Jewelleis,  &c.  By 
James  E.  Collins.  i8mo,  cloth 75 

CIPHER  AND  SECRET  LETTER  AND  TELE- 
GRAPHIC CODE,  with  Hogg's  Improvements. 
The  most  perfect  secret  code  ever  invented  or  dis- 
covered. Impossible  to  read  without  the  key.  By 
C.  S.  Larrabee.  iSmo,  cloth i  oo 

COLBURN.  The  Gas  Works  of  London.  By  Zerah 

Colburn,  C.  E.  i  vol.  izmo,  boards 60 

CRAIG  (B.  F.)  Weights  and  Measures.  An  account 
of  the  Decimal  System,  with  Tables  of  Conversion 
for  Commercial  and  Scientific  Uses.  By  B.  F.  Craig, 
M.D.  i  vol.  square  3zmo,  limp  cloth. ...  50 

NUGENT.  Treatise  on  Optics;  or,  Light  and  Sight, 
theoretically  and  practically  treated ;  with  the  appli- 
cation to  Fine  Art  and  Industrial  Pursuits.  By  E. 
Nugent.  With  one  hundred  and  three  illustrations. 
J2mo,  cloth 2°° 

GLYNN  (J.)  Treatise  on  the  Power  of  Water,  as  ap- 
plied to  drive  Flour  Mills,  and  to  give  motion  to 
Turbines  and  other  Hydrostatic  Engines.  By  J  oseph 


D.  VAN    NOSTBAXD  S   Pr 


Glynn.     Third  edition,   revised  and  enlarged,  with 
numerous  illustrations.     i2mo,  cloth  ............    .  |!i   oo 

HUMBER.  A  Handy  Book  for  the  Calculation  of 
Strains  in  Girders  and  similar  Structures,  and  their 
Strength,  consisting  of  Formulae  and  corresponding 
Diagrams,  with  numerous  details  for  practical  appli- 
cation. By  William  H  umber.  izmo,  fully  illus- 
trated, cloth  .....................................  2  50 

GRUNER.  The  Manufacture  of  Steel.  By  M.  L. 
Gruner.  Translated  from  the  French,  by  Lenox 
Smith,  with  an  appendix  on  the  Bessamer  process  in 
the  United  States,  by  the  translator.  Illustrated  by 
Lithographed  drawings  and  wood  cuts.  8vo,  cloth.  .  3  50 

AUCHINCI.OSS.  Link  and  Valve  Motions  Simplified. 
Illustrated  with  37  wood-cuts,  and  21  lithographic 
plates,  together  with  a  Travel  Scale,  and  numerous 
useful  Tables.  By  W.  S.  Auchincloss.  8vo,  cloth..  3  oo 

VAN  BUR  EN.  Investigations  of  Formulas,  for  the 
strength  of  the  Iron  parts  of  Steam  Machinery.  By 
J.  D.  Van  Buren,  Jr.,  C.  E.  Illustrated,  iivo,  cloth.  2  oo 

JOYNSON.  Designing  and  Construction  of  Machine 

Gearing.  Illustrated,  8vo,  cloth  .........  ........  2  oo 

GILLMORE.  Coignet  Betonand  other  Artificial  Stone. 
By  Q.  A.  Gill  more,  Major  U  S.  Corps  Engineers. 
9  plates,  views,  &c.  Svo,  cloth  ....................  2  50 

SAELTZER.  Treatise  on  Acoustics  in  connection  with 
Ventilation.  By  Alexander  Saeltzer,  Architect. 
I2mo,  cloth  ......................................  2  oo 

THE  EARTH'S  CRUST.  A  handy  Outline  of  Geo- 

logy. By  David  Page.  Illustrated,  iSmo,  cloth  ----  75 

DICTIONARY  of  Manufactures,  Mining,  Machinery, 
and  the  Industrial  Arts.  By  George  Dodd.  i2mo, 
cloth  ............................................  2  oo 

FRANCIS.  On  the  Strength  of  Cast-Iron  Pillars,  with 
Tables  for  the  use  of  Engineers,  Architects,  and 
Builders.  By  James  B.  Francis,  Civil  Engineer. 
i  vol.  Svo,  cloth  ..................................  2  '« 


D.  TAN   NOSIRAND  S   PUBLICATIONS. 

•GILLMORE  (Gen.  Q.  A.)  Treatise  on  Limes,  Hy 
dr;  ulic  Cements,  and  Mortars.  Papers  on  Practical 
Engineering,  U.  S.  Engineer  Department,  No.  9, 
containing  Reports  of  numerous  Experiments  con- 
ducted in  New  York  City,  during  the  years  1858  iff 
1861,  inclusive.  By  Q.  A.  Gillmore,  Bvt.  Maj  -Gen., 
U.  S.  A.,  Major,  Corps  of  Engineers.  With  num- 
erous illustrations,  i  vol,  8vo,  cloth $4  oo 

HARRISON.  The  Mechanic's  Tool  Book,  with  Prac- 
tical Rules  and  Suggestions  for  Use  of  Machinists, 
Iron  Workers,  and  others.  By  W.  B.  Harrison, 
associate  editor  of  the  "American  Artisan."  Illus- 
trated with  44  engravings,  ismo,  cloth x  50 

HENRICI  (Olaus).  Skeleton  Structures,  especially  in 
their  application  to  the  Building  of  Steel  and  Iron 
Bridges.  By  Olaus  Henrici.  With  folding  plates 
and  diagrams,  i  vol.  8vo,  cloth  .• 3  oo 

.HEWSON  (Wm.)  Principles  and  Practice  of  Embank 
ing  Lands  from  River  Floods,  as  applied  to  the  Le- 
vees of  the  Mississippi.  By  William  Hewson,  Civil 
Engineer,  i  vol.  8 vo,  cloth 2  oo 

HOLLEY  (A.  L.)  Railway  Practice.  American  and 
European  Railway  Practice,  in  the  economical  Gen- 
eration of  Stearr,  including  the  Materials  and  Con- 
struction of  Coal-burning  Boilers,  Combustion,  the 
Variable  Blast,  Vaporization,  Circulation,  Superheat- 
ing, Supplying  and  Heating  Feed-water,  etc.,  and 
the  Adaptation  of  Wood  and  Coke-burning  Engines 
to  Coal-burning  ;  and  in  Permanent  Way,  including 
Road-bed,  Sleepers,  Raiis,  Joint-fastenings,  Street 
Railways,  etc.,  etc.  By  Alexander  L.  Holley,  B.  P. 
With  77  lithographed  plates,  i  vol.  folio,  cloth. ...  13  oo 

KING  (W.  H.)  Lessons  and  Practical  Notes  on  Steam, 
the  Steam  Engine,  Propellers,  etc.,  etc.,  for  Young 
Marine  Engineers,  Students,  ar.d  others.  By  the 
late  W.  H.  King,  U.  S.  Navy.  Revised  by  Chief 
Engineer  J.  W.  King,  U.  S.  Navy.  Twelfth  edition, 
enlarged.  8vo,  cloth a  oo 

MINIFIE(Wm.)  Mechanical  Drawing.  A  Text- Book 
af  Geometrical  Drawing  for  the  use  of  Mechanic* 

4 


£..   VAN   NOSTHANDS   PUBLICATIONS. 

«n&  Schools,  in  which  the  Definitions  and  Rules  or 
Geometry  are  familiarly  explained ;  the  Practical 
Problems  are  arranged,  from  the  most  simple  to  the 
more  complex,  and  in  their  description  technicalities 
are  avoided  as  much  as  possible.  With  illustrations 
for  Drawing  Plans,  Sections,  and  Elevations  of  Rail- 
ways and  Machinery ;  an  Introduction  to  Isometrical 
Drawing,  and  an  Essay  on  Linear  Perspective  and 
Shadows.  Illustrated  with  over  200  diagrams  en- 
graved on  steel.  By  Wm.  Minifie,  Architect.  Sev- 
enth edition.  With  an  Appendix  on  the  Theory  and 

Application  of  Colors,     i  vol.  8vo,  cloth $4  oo 

"It  la  the  best  work  on  Drawing  that  we  have  ever  seen,  and  i» 
especially  a  text-book  of  Geometrical  Drawing  tor  the  use  of  Mechanics 
and  Schools.  No  young  Mechanic,  such  as  a  Machinists,  Engineer,  Cabi- 
net-maker, Millwright,  or  Carpenter,  should  be  without  It."— Sevnl(/ie 


•  Geometrical  Drawing.     Abridged  from  the  octavo 


edition,  for  the  use  of  Schools.  Illustrated  with  48 
steel  plates.  Fifth  edition,  i  voL  121110,  cloth....  a  oo 

STILLMAN  (Paul.)  Steam  Engine  Indicator,  and  the 
Improved  Manometer  Steam  and  Vacuum  Gauges—- 
their Utility  and  Application.  By  Paul  Stillman. 
New  edition,  i  vol.  121110,  flexible  cloth i  oo 

SWEET  (S.  H.)  Special  Report  on  Coal ;  showing  its 
Distribution,  Classification,  and  cost  delivered  over 
different  routes  to  various  points  in  the  State  of  New 
York,  and  the  principal  cities  on  the  Atlantic  Coast. 
By  S.  H.  Sweet  With  maps,  i  vol.  8vo,  cloth 3  oo 

WALKER  (W.  H.)  Screw  Propulsion.  Notes  on 
Screw  Propulsion  :  its  Risa  and  History.  By  Capt. 
W.  H.  Walker,  U.  S.  Navy,  i  vol.  8vo,  cloth 75 

WARD  (J.  H.)  Steam  for  the  Million.  A  popular 
Treatise  on  Steam  and  its  Application  to  the  Useful 
Arts,  especially  to  Navigation.  By  J.  H.  Ward, 
Commander  U.  S.  Navy.  New  and  revised  edition, 
i  vol.  8vo,  cloth i  oo 

WEISBACH  (Julius).  Principles  of  the  Mechanics  of 
Machinery  and  Engineering.  By  Dr.  Julius  Weis- 
bach,  of  Freiburg.  Translated  from  the  last  German 
edition,  i  Vol.  I.,  8vo,  cloth 10  oo 


t>.  VAN  KCSTEAND'S  PUBLICATIONS. 

DIEDRICH.  The  Theory  of  Strains,  a  Compendium 
for  the  calculation  and  construction  of  Bridges,  Hoofs, 
and  C'raues,  with  the  app'ication  of  Trigonometrical 
?;otes,  containing  the  most  comprehensive  informa- 
tion in  regard  to  the  Resulting  strains  fur  a  peimaii- 
ent  Load,  as  aiso  for  a  combined  (Permanent  and 
llolling)  Load  In  two  sections,  adadted  to  the  re- 
quirements of  the  present  time.  By  John  D'edrich, 
0.  E.  Illustrated  by  numerous  plates  and  diagrams. 
8vo,  cloth 5  oo 

WILLIAMSON  (R.  S.)  On  the  use  of  the  Barometer  on 
Surveys  and  Reconnoissances.  Part  I.  Meteorology 
in  its  Connection  with  Hypsometry.  Part  II.  Baro- 
metric Hypsometry.  By  R.  S.  Wiliamson,  Bvt. 
Lieut. -Col.  U.  S.  A.,  Major  Corps  of  Engineers. 
With  Illustrative  Tables  and  Engravings.  Paper 
No.  15,  Professional  Papers,  Corps  of  Engineers, 
i  vol.  410,  cloth 15  oo 

POOK  (S.  M.)  Method  of  Comparing  the  Lines  and 
Draughting  Vessels  Propelled  by  Sail  or  Steam. 
Including  a  chapter  on  Laying  off  on  the  Mould- 
Loft  Floor.  By  Samuel  M.  Pook,  Naval  Construc- 
tor, i  vol.  Svo,  with  illustrations,  cloth 5  oo 

ALEXANDER  (J.  H.)  Universal  Dictionary  of 
Weights  and  Measures,  Ancient  and  Modern,  re- 
duced to  the  standards  of  the  United  States  of  Ame- 
rica. By  J.  H.  Alexander.  New  edition,  enlarged. 
i  voL  8vo,  cloth 3  50 

BROOKLYN  WATER  WORKS.  Containing  a  De- 
scriptive Account  of  the  Construction  of  the  Works, 
and  also  Reports  on  the  Brooklyn,  Hartford,  Belie- 
yille  and  Cambridge  Pumping  Engines.  With  illustra- 
tions, i  vol.  folio,  cloth 30  oo 

RICHARDS'  INDICATOR.  A  Treatise  on  the  Rich- 
ards Steam  Engine  Indicator,  with  an  Appendix  by 
F.  W.  Bacon,  M.  E.  i8mo,  flexible,  cloth i  oo 

6 


D.  VAN  NOSTKAND'S  PUBLICATIONS, 

POPE.  Modern  Practice  of  the  Electric  Telegraph.  A 
Hand  Book  for  Electricians  and  operators.  By  Frank 
L.  Pope.  Eighth  edition,  revised  and  enlarged,  and 

fully  illustrated.     8vo,  cloth $2.00 

"  There  is  no  other  work  of  this  kind  In  the  EnRlUh  langusse  th»t  con- 
tains ia  so  small  acompatsso  much  p.artical  iu!»rniaii»n  in  the  appli- 
cation of  galvanic  electricity  to  telegraphy.  It  sli.  nl.l  ba  in  the  h,ui,ls  of 
tTsryoue  iutertsted  ia  telegraphy,  or  tUe  uee  ...f  Batteries  for  other  pur- 
poses." 

MORSE.  Examination  of  the  Telegraphic  Apparatus 
and  the  Processes  in  Telegraphy.  By  Samuel  F. 
Morse,  LL.D.,  U-  S.  Commissioner  P.tris  Universal 
Exposition,  1867.  Illustrated,  Svo,  cloth $2  oo 

SABINE.  History  and  Progress  of  the  Klectric  Tele- 
graph, with  descriptions  of  some  of  the  apparatus. 
By  Robert  Sabine,  C.  E.  Second  edition,  with  ad- 
ditions, izmo,  cloth i  25 

CULLEY.  A  Hand-Book  of  Practical  Telegraphy.  By 
R.  S.  Culley,  Engineer  to  the  Electric  and  Interna- 
tional Telegraph  Company.  Fourth  edition,  revised 
and  enlarged,  illustrated  Svo,  cloth 500 

BENET.  Electro-Ballistic  Machines,  and  the  Schultz 
Chronoscope.  By  Lieut. -Col.  S.  V  Benet,  Captain 
of  Ordnance,  U.  S.  Army.  Illustrated,  second  edi- 
tion, 410,  cloth 3  oo 

MICHAELIS.  The  Le  Poulenge  Chronograph,  with 
three  Lithograph  folding  plates  of  illustrations.  By 
Brevet  Captain  O.  E.  Michaelis,  First  Lieutenant 
Ordnance  Corps,  U.  S.  Army,  410,  cloth 3  oo 

ENGINEERING  FACTS  AND  FIGURES  An 
Annual  Register  of  I'rogress  in  Mechanical  Engineer- 
ing and  Construction  for  the  years  1863,  64,  65.  66, 
67,  68.  Fully  illustrated,  6  vols.  i8mo,  cloth,  $2.50 
per  vol.,  each  volume  sold  separately 

HAMILTON.  Useful  Information  for  Railway  Men. 
Compiled  by  W.  G.  Hamilton,  Engineer.  Kifth  edi- 
tion, revised  and  enlarged,  562  pages  Pocket  form. 
Morocco,  gilt 2  oo 


D.  VAX  NOSTUAND  S  PUBLICATIONS. 


STUART.  The  Civil  and  Military  Engineers  of  Amer- 
ica. By  Gen.  C.  B.  Stuart  With  9  finely  executed 
portraits  of  eminent  engineers,  and  illustrated  by 
engravings  of  some  of  the  most  important  works  con- 
structed in  America.  8vo,  cloth $5  oo 

STONEY.  The  Theory  of  Strains  in  Girders  and  simi- 
lar structures,  with  observations  on  the  application  of 
Theory  to  P-actice,  and  Tables  of  Strength  and  other 
properties  of  Materials.  By  Uindon  B.  Stoney,  B.  A. 
New  and  revised  edition,  enlarged,  with  numerous 
engravings  on  wood,  by  Oldham.  Royal  8vo,  664 
pages.  Complete  in  one  volume.  8vo,  cloth 1500 

SHREVE.  A  Treatise  on  the  Strength  of  Bridges  and 
Roofs.  Comprising  the  determination  of  Algebraic 
formulas  for  strains  in  Horizontal,  Inclined  or  Rafter. 
Triangular,  Bowstring,  Lenticular  and  other  Trusses, 
from  fixed  and  moving  loads,  with  practical  applica- 
tions and  examples,  for  the  use  of  Students  and  Engi- 
neers. By  Samuel  H.  Shreve,  A.  M.,  Civil  Engineer. 
87  wood  cut  illustrations.  8vo,  cloth 5  oo 

MERRILL.  Iron  Truss  Bridges  for  Railroads.  The 
method  of  calculating;  strains  in  Trusses,  with  a  care- 
ful comparison  of  the  most  prominent  Trusses,  in 
reference  to  economy  in  combination,  etc.,  etc  By 
Brevet  Col.  William  E.  Merrill,  U  S.  A.,  Major 
Corps  of  Engineers,  with  nine  lithographed  plates  of 
Illustrations.  410,  cloth 500 

WHIPPLE.  An  Elementary  and  Practical  Treatise  on 
Bridge  Building.  An  enlarged  and  improved  edition 
of  the  author's  original  work.  By  S.  Whipple,  C.  E  , 
inventor  of  the  Whipple  Bridges,  &c.  Illustrated 
8vo,  cloth 4  oo 

THE  KANSAS  CITY  BRIDGE.  With  an  account 
of  the  Regimen  of  the  Missouri  River,  and  a  descrip- 
tion of  the  methods  used  for  Founding  in  that  River. 
ByO  Chanute,  Chief  Engineer,  and  George  Morri- 
son, Assistant  Engineer.  Illustrated  with  five  litho- 
graphic views  aid  twelve  plates  of  plans.  410,  cloth,  6  oo 


D.  VAIT  IxOSTUAND  S 


MAC  CORD.  A  Practical  Treatise  on  the  Slide  Valve 
by  Eccentrics,  examining  by  methods  the  action  of  the 
Eccentric  upon  the  Slide  Valve,  and  explaining  the 
Practical  processes  of  laying  out  the  movements, 
adapting  the  valve  for  its  various  duties  in  the  steam 
engine.  For  the  use  of  Engineers,  Draughtsmen) 
Machinists,  and  Students  of  Valve  Motions  in  gene- 
ral. ByC.W.  Mac  Cord,  A.  M;,  Professor  of  Me- 
chanical Drawing,  Stevens'  Institute  of  Technology! 
Hoboken,  N.  J.  Illustrated  by  8  full  page  copper- 
plates. 4to,  cloth $4  oo 

K.IRKWOOD.  Report  on  the  Filtration  of  River 
Waters,  for  the  supply  of  cities,  as  practised  in 
Europe,  made  to  the  Board  of  Water  Commissioners 
of  the  City  of  St.  Louis.  By  James  P.  Kirkwood. 
Illustrated  by  30  double  p!ate  engravings.  410,  cloth,  1500 

PLATTNER.  Manual  of  Qualitative  and  Quantitative 
Analysis  with  the  Blow  I  ipe.  From  the  last  German 
edition,  revised  and  enlarged.  By  Prof.  Th.  Richter, 
of  the  Royal  Saxon  Mining  Academy.  Translated 
by  Prof.  H.  B.  Cornwall,  Assistant  in  the  Columbia 
School  of  Mines,  New  York  assisted  by  John  H. 
Caswell.  Illustrated  with  87  wood  cuts,  and  one 
lithographic  plate.  Second  edition>  revised,  560 
pages,  8vo,  cloth 7  50 

PLYMPTON.  The  Blow  Pipe.  A  system  of  Instruc- 
tion in  its  practical  use  being  a  graduated  course  of 
analysis  for  the  use  of  students,  and  all  those  engaged 
in  the  examination  of  metallic  combinations  Second 
edition,  with  an  appendix  and  a  copious  index.  By 
Prof.  Geo  W.  Plympton,  of  the  Polytechnic  Insti- 
tute, Brooklyn,  N.  Y.  umo,  cloth 300 

PYNCHON.  Introduction  to  Chemical  Physics,  design- 
ed for  the  use  of  Academies,  Colleges  and  High 
Schools.  Illustrated  with  numerous  engravings, and 
containing  copious  experiments  with  directions  for 
preparing  them.  By  Thomas  Ruggles  Pynchon, 
M.  A.,  Professor  of  Chemistry  and  the  Natural  Sci- 
ences, Trinity  College,  Hartford  New  edition,  re- 
vised and  enlarged  and  illustrated  by  269  illustrations 

on  wood.     Crown,  8 vo.  cloth 300 

9 


D.  VAN  NOSTRAND'S  PUBLICATIONS. 

ELIOT  AND  STORER.  A  compendious  Manual  of 
Qualitative  Chemical  Analysis.  By  Charles  W. 
Eliot  and  Frank  H.  Storer.  Revised  with  the  Co- 
operation of  the  authors.  By  William  R.  Nichols, 
Professor  of  Chemistry  in  the  Massachusetts  Insti- 
tute of  Technology  Illustrated,  I2mo,  cloth $i  50 

RAMMELSBERG.  Guide  to  a  course  of  Quantitative 
Chemical  Analysis,  especially  of  -Minerals  and  Fur- 
nace Products.  Illustrated  by  Examples  By  C  F. 
Rammelsberg.  Translated  by  J.  Towler,  M.  D. 
8vo,  cloth 2  25 

EGLESTON.  Lectures  on  Descriptive  Mineralogy,  de- 
livered at  the  School  of  Mines.  Columbia  College. 
By  Professor  T.  Kgleston.  Illustrated  by  34  Litho- 
graphic Plates.  8vo,  cloth 4  50 

MITCHELL.  A  Manual  of  Practical  Assaying.  By 
John  Mitchell.  Third  edition.  Edited  by  William 
Crookes,  F.  R.  S.  8vo,  cloth to  oo 

WATT'S  Dictionary  of  Chemistry.  New  and  Revised 
edition  complete  in  6  vols  8vo  cloth,  $62.00  Sup- 
plementary volume  sold  separately.  1'rice,  cloth...  9  oo 

RANDALL.  Quartz  Operators  Hand-Book.  By  P.  M. 
Randall.  New  edition,  revised  and  enlarged,  fully 
illustrated.  12010,  doth 200 

SILVERSMITH.  A  Practical  Hand-Book  for  Miners, 
Metallurgists,  and  Assayers,  comprising  the  most  re- 
cent improvements  in  the  disintegration,  amalgama- 
tion, smelting,  and  parting  of  the  i  recious  ores,  with 
a  comprehensive  Digest  of  the  Mining  Laws.  Greatly 
augmented,  revised  and  corrected.  By  Julius  Silver- 
smith. Fourth  edition.  Profusely  illustrated.  12010, 
cloth 3  o* 

THE  USEFUL  METALS  AND  THEIR  ALLOYS, 
including  Mining  Ventilation,  Mining  Jurisprudence, 
and  Metallurgic  Chemistry  employed  in  the  conver- 
sion of  Iron,  Copper,  Tin,  Zinc,  Antimony  and  Lead 
ores,  with  their  applications  to  the  Industrial  Arts. 
By  Scoffren,  Truan,  Clay,  Oxland,  Fairbairn,  and 

others.     Fifth  edition,  half  calf 375 

10 


D.  VAN  NOSTItAND  8  PUBLICATIONS. 

JOVNSON.  The  Metals  used  in  construction,  Iron, 
Steei,  Bessemer  Metal,  etc.,  etc.  By  F.  H.  Joynson. 
Illustrated,  12010,  cloth $o  75 

VON  COTTA.  Treatise  on  Ore  Deposits.  By  Bern- 
hard  Von  Cotta,  Professor  of  Geology  in  the  Royal 
School  of  Mines,  Freidberg,  Saxony.  Translated 
from  the  second  German  edition,  by  Frederick 
Prime,  Jr.,  Mining  Engineer,  and  revised  by  the  au- 
thor, with  numerous  illustrations.  8vo,  cloth 400 

URE.  Dictionary  of  Arts,  Manufactures  and  Mines. '  By 
Andrew  Ure,  M.D.  Sixth  edition,  edited  by  Robert 
Hunt,  F.  R.  S.,  greatly  enlarged  and  re-written. 
London,  1872.  3  vols.  8vo,  cloth,  $25.00.  Half 
Russia 37  50 

BELL.  Chemical  Phenomena  of  Iron  Smelting.  An 
experimental  and  practical  examination  of  the  cir- 
cumstances which  determine  die  capacity  of  the  Blast 
Furnace,  The  Temperature  of  the  air,  and  the 
proper  condition  of  the  Materials  to  be  operated 
upon.  By  I.  Lowthian  Bell.  8 vo,  cloth 600 

ROGERS.  The  Geology  of  Pennsylvania.  A  Govern- 
ment survey,  with  a  general  view  of  the  Geology  of 
the  United  States,  Essayi  on  the  Coal  Formation  and 
its  Fossils,  and  a  description  of  the  Coal  Fields  of 
North  America  and  Great  Britain.  By  Henry  Dar- 
win Rogers,  late  State  Geologist  of  Pennsylvania, 
Splendidly  illustrated  with  Plates  and  Engravings  in 
the  text.  3  vols.,  410,  cloth,  with  Portfolio  of  Maps.  30  oo 

BURGH.  Modern  Marine  Engineering,  applied  to 
Paddle  and  Screw  Propulsion.  Consisting  of  36 
:olored  plates,  259  Practical  Wood  Cut  Illustrations, 
and  403  pages  ol  descriptive  matter,  the  whole  being 
an  exposition  of  the  present  practice  of  James 
Watt  &  Co.,  J.  &  G.  Rennie,  R.  Napier  &  Sons, 
and  other  celebrated  firms,  by  N.  F.  Burgh,  Engi- 
neer, thick  410,  vol.,  cloth,  $25.00 ;  half  mor 30  oo 

BARTOL.  Treatise  on  the  Marine  Boilers  of  the  United 

States.    By  B.  H.  Bartol.    Illustrated,  8vo,  cloth.. .     150 
II 


D.  VAN  NOSTRAND'S  PUBLICATIONS. 

BOURNE.  Treatise  on  the  Steam  Engine  in  its  various 
applications  to  Mines,  Mills,  Steam  Navigation, 
Railways,  and  Agriculture,  with  the  theoretical  in- 
vestigations respecting  the  Motive  Power  of  Heat, 
and  the  proper  proportions  of  steam  engines.  Elabo- 
rate tables  of  the  right  dimensions  of  every  part,  and 
Practical  Instructions  for  the  manufacture  and  man- 
agement of  every  species  of  Engine  in  actual  use. 
By  John  Bourne,  being  the  ninth  edition  of  "  A 
Treatise  on  the  Steam  Engine,"  by  the  "  Artizan 
Club."  Illustrated  by  38  plates  and  546  wood  cuts. 
4to,  cloth $15  oo 

STUART.  The  Naval  Dry  Docks  of  the  United 
Slates.  By  Charles  B.  Stuart  late  Engineer-in-Cbief 
of  the  U.  S.  Navy.  Illustrated  with  24  engravings 
on  steel.  Fourth  edition,  cloth 6  oo 

EADS.     System  of  Naval   Defences.      By  James  B. 

Eads,  C.  E.,  with  10  illustrations,  410,  cloth 5  oo 

FOSTER.  Submarine  Blasting  in  Boston  Harbor, 
Massachusetts.  Removal  of  Tower  and  Corwin 
Rocks.  By  J.  G.  Foster,  Lieut -Col.  of  Engineers, 
U-  S.  Army.  Illustrated  with  seven  plates,  410, 
cloth 3  50 

BARNES  Submarine  Warfare,  offensive  and  defensive, 
including  a  discussion  of  the  offensive  Torpedo  Sys- 
tem, its  effects  upon  Iron  Clad  Ship  Systems  and  in- 
fluence upon  future  naval  wars.  By  Lieut. -Com- 
mander J.  S.  Barnes,  U.  S.  N.,  with  twenty  litho- 
graphic plates  and  many  wood  cuts.  8vo,  cloth 5  oo 

HOLLEY.  A  Treatise  on  Ordnance  and  Armor,  em- 
bracing descriptions,  discussions,  and  professional 
opinions  concerning  the  materials,  fabrication,  re- 
quirements, capabilities,  and  endurance  of  European 
and  American  Guns,  for  Naval,  Sea  Coast,  and  Iron 
Clad  Warfare,  and  their  Rifling,  Projectiles,  and 
Breech- Loading;  also,  results  of  experiments  against 
armor,  from  official  records,  with  an  appendix  refer- 
ring to  Gun  Cotton,  Hooped  Guns,  etc.,  etc.  By 
Alexander  L.  Holley,  B.  P.,  948  pages,  493  engrav- 
ings, and  147  Tables  of  Results,  etc.,  8vo,  half  roan,  to  oo 
12 


D.  VAN  NOSTRAND'S  PUBLICATIONS. 

.  A  Treatise  on  the  Principles  and  Practice  of 
Levelling,  showing  its  application  to  purposes  of 
Railway  Engineering  and  the  Construction  of  Roads, 
&c-  By  Frederick  W.  Simms,  0.  E.  From  the  sth 
London  edition,  revised  and  corrected,  with  the  addi- 
tion of  Mr.  Laws's  Practical  Examples  for  setting 
out  Railway  Curves.  Illustrated  with  three  Litho- 
graphic plates  and  numerous  wood  cuts.  8vo,  cloth.  $2  jo 
BURT.  Key  to  the  Solar  Compass,  and  Surveyor's 
Companion ;  comprising  all  the  rules  necessary  for 
use  in  the  field ;  also  description  of  the  Linear  Sur- 
reys and  Public  Land  System  of  the  United  States, 
Notes  on  the  Barometer,  suggestions  for  an  outfit  for 
a  survey  of  four  months,  etc-  By  W.  A.  Hurt,  U.  S. 
Deputy  Surveyor.  Second  edition.  Pocket  book 
form,  tuck. ao  50 

THE  PLANE  TABLE.  Its  uses  in  Topographical 
Surveying,  from  the  Papers  of  the  U.  S.  Coast  Sur- 
vey. Illustrated,  8vo,  cloth 2  co 

"  This  worK  gives  a   description  of  the  Plane  Ttble,  employed  at  Ui« 
17.  S.  Gout  Survey  office,  and  the  manner  of  using  it." 

JEFFER'S.  Nautical  Surveying.  By  W.  N.  Jeffers, 
Captain  U.  S.  Navy.  Illustrated  with  9  copperplates 
and  31  wood  cut  illustrations.  8vo,  cloth 3  oo 

CHAUVENET.  New  method  of  correcting  Lunar  Dis- 
tances, and  improved  method  of  Finding  the  error 
and  rate  of  a  chronometer,  by  equal  altitudes.  By 
W.  Chauvenet,  LL.D.  8vo,  cloth a  oo 

BRUNNOW.  Spherical  Astronomy.  By  F.  Brunnow, 
Ph.  Dr.  Translated  by  the  author  from  the  second 
German  edition.  8vo,  cloth 650 

PEIRCE.  System  of  Analytic  Mechanics.  By  Ben- 
jamin Peirce.  410,  cloth 10  oo 

COFFIN.  Navigation  and  Nautical  Astronomy.  Pre- 
pared for  the  use  of  the  U.  S.  Naval  Academy.  By 
Prof.  J.  H.  C.  Coffin.  Fifth  edition.  52  wood  cut  illus- 
trations, izmo,  cloth ,. . , 3  5» 

13 


D.  VAN  NOSTRAND  S  PUBLICATIONS. 

CLARK.  Theoretical  Navigation  and  Nautical  Astron- 
omy. By  Lieut.  Lewis  Ulark,  U.  S.  N.  Illustrated 
with  41  wood  cuts.  Svo,  cloth $300 

HASKINS.  The  Galvanometer  and  its  Uses.  A  Man- 
ual for  Electricians  and  Students.  By  C.  H.  Has- 
kins.  lamo,  pocket  form,  morocco.  (In  press) 

GOUGE.  New  System  of  Ventilation,  which  has  been 
thoroughly  tested,  under  the  patronage  of  many  dis- 
tinguished persons.  By  Henry  A.  Gouge.  With 
many  illustrations.  Svo,  cloth 200 

BECKWITH.  Observations  on  the  Materials  and 
Manufacture  of  Terra-Cotta,  Stone  Ware,  Fire  Brick, 
Porcelain  and  Encaustic  Tiles,  with  remarks  on  the 

Eroducts  exhibited  at  the  London  International  Exhi- 
ition,   1871.      By  Arthur  Beckwith,   C.    E.      Svo, 
paper 60 

MORFIT.  A  Practical  Treatise  on  Pure  Fertilizers,  and 
the  chemical  conversipn  of  Rock  Guano,  Marlstones, 
Coprolites.  and  the  Crude  Phosphates  of  Lime  and 
Alumina  generally,  into  various  valuable  products. 
By  Campbell  Morfit,  M.D.,  with  28  illustrative  plates, 
Svo,  cloth 2oo« 

BARNARD.  The  Metric  System  of  Weights  and 
Measures.  An  address  delivered  before  the  convoca- 
tion of  the  University  of  the  State  of  New  York,  at 
Albany,  August,  1871.  By  F.  A  P.  Barnard.  LL.D., 
President  of  Columbia  College,  New  York,  Second 
edition  from  the  revised  edition,  printed  for  the  Trus- 
tees of  Columbia  College.  Tinted  paper,  Svo,  cloth  3  oe 

•  Report  on  Machinery  and  Processes  on  the  In- 
dustrial Arts  and  Apparatus  of  the  Exact  Sciences. 
By  F.  A.  P.  Barnard,  LL.  D.  Paris  Universal  Ex- 
position, 1867.  Illustrated,  Svo,  cloth 5  oo 

BARLOW.  Tables  of  Squares,  Cubes,  Square  Roots, 
Cube  Roots,  Reciprocals  of  all  integer  numbers  up  tn 

10,000.     New  edition,  izmo,  cloth 250 

14 


D.  VAN  NOSTRAND'S  PUBLICATIONS. 

MYER.  Manual  of  Signals,  for  the  use  of  Signal  officers 
in  the  Field,  and  for  Military  and  Naval  Students, 
Military  Schools,  etc-  A  new  edition  enlarged  and 
illustrated.  By  Brig.  General  Albert  J.  Myer,  Chief 
Signal  Officer  of  the  army,  Colonel  of  the  Signal 
Corps  during  the  War  of  the  Rebellion.  i2mo,  48 
plates,  full  Roan $5  oo 

WILLIAMSON.  Practical  Tables  in  Meteorology  and 
Hypsometry,  in  connection  with  the  use  of  the  Bar- 
ometer. By  CoL  R.  S.  Williamson,  U.  S.  A.  410, 
cloth 2  50 

THE  YOUNG  MECHANIC.  Containing  directions 
for  the  use  of  all  kinds  of  tools,  and  for  the  construc- 
tion of  Steam  Engines  and  Mechanical  Models,  in- 
cluding the  Art  of  Turning  in  Wood  and  Metal.  By 
the  author  "  The  Lathe  and  its  Uses,"  etc.  From 
the  English  edition  with  corrections.  Illustrated, 
J2mo,  cloth... i  75 

PICKERT  AND  METCALF.  The  Art  of  Graining. 
How  Acquired  and  How  Produced,  with  description 
of  colors,  and  their  application.  By  Charles  Pickert 
and  Abraham  Metcalf  Beautifully  illustrated  with 
42  tinted  plates  of  the  various  woods  used  in  interior 
finishing.  Tinted  paper,  410,  cloth 10  oo 

HUNT.  Designs  for  the  Gateways  of  the  Southern  En- 
trances to  the  Central  Park.  'By  Richard  M.  Hunt. 
With  a  description  of  the  designs.  410.  cloth 500 

LAZELLE.  One  Law  in  Nature.  By  Capt.  H.  M. 
Lazelle,  U.  S.  A.  A  new  Corpuscular  Theory,  com- 
prehending Unity  of  Force,  Identity  of  Matter,  and 
its  Multiple  Atom  Constitution,  applied  to  the  Physi- 
cal Affections  or  Modes  of  Energy.  12010,  cloth. . .  i  50 

PETERS.  Notes  on  the  Origin,  Nature,  Prevention, 
and  Treatment  of  Asiatic  Cholera.  By  John  C. 
Peters,  M.  D.  Second  edition,  with  an  Appendix. 
I2tno,  cloth i  5° 


D.  VAN  NOSTRAND  8  PUBLICATIONS. 

BOYNTON.  History  of  West  Point,  its  Military  Im- 
portance during  the  American  Revolution,  and  the 
Origin  and  History  of  the  U.  S.  Military  Academy. 
By  Bvt  .Major  C.  E.  Boynton,  A.M.,  Adjutant  of  the 
Military  Academy.  Second  edition,  416  pp.  8yo, 
printed  on  tinted  paper,  beautifully  illustrated  with 
36  maps  and  fine  engravings,  chiefly  from  photo- 
graphs taken  on  the  spot  by  the  author.  Extra 
cloth $3  50 

WOOD.  West  Point  Scrap  Book,  being  a  collection  of 
Legends,  Stories,  Songs,  etc,  of  the  U  S  Military 
Academy.  My  Lieut  O  E.  Wood,  U.  S.  A.  Illus- 
trated by  69  engravings  and  a  copperplate  map. 
Beautifully  printed  on  tinted  paper.  8vo,  cloth 5  oo 

WEST  POINT  LIFE.  A  Poem  read  before  the  Dia- 
lectic Society  of  the  United  States  Military  Academy. 
Illustiated  with  Pen-and-ink  Sketches.  By  a  Cadet 
To  which  is  added  the  song,  *'  Benny  Havens,  oh  1" 
oblong  Svo,  21  full  page  illustrations,  cloth. 2  50 

GUIDE  TO  WEST  POINT  and  the  U.  S.  Military 
Academy,  with  maps  and  engravings,  iSmo,  blue 
cloth,  flexible i  oo 

HENRY.  Military  Record  of  Civilian  Appointments  in 
the  United  States  Army  By  Guy  V.  Henry,  Brevet 
Colonel  and  Captain  First  United  States  Artillery, 
Late  Colonel  and  Brevet  Brigadier  General,  United 
States  Volunteers.  Vol.  i  now  ready.  VoL  a  in 
press.  Svo,  per  volume,  cloth 5  00 

HAMERSLY.  Records  of  Living  Officers  of  the  U. 
S.  Navy  and  Marine  Corps.  Compiled  from  official 
sources.  By  Lewis  B.  Hamersly,  late  Lieutenant 
U-  S.  Marine  Corps.  Revised  edition,  8vo,  cloth ...  50* 

MOORE.  Portrait  Gallery  of  the  V^ar.  Civil,  Military 
and  Naval.  A  Biographical  record,  edited  by  Frank 
Moore.  60  fine  portraits  on  steel.  Royal  8vo, 
cloth 6  o* 

16 


OCSB  LIBRARY 


A     nnn     "''''I'li 


VAN  NOSTRAND'SJfilENCE  SEEIES, 

It  is  the  ii'teiition  of  tlif  Publisher  of  this  Series  to 

issue  them  ;it  intervals  of  about  a  month.     They  will 

ii  a  uniform,  ueal,  and  attr: vthu  form,  ami 

will  U>  sold  at  .rj()  cents.     The  subject.,  v.  ill   be  of  an 

e.miiiently  Scientific  character,  and   embrace,  as  wide  a 

of   topics   as   possible,    all    of    the    v 
order. 

No.  1.— CHIMNEYS     KOJf.     I-'ITRNA(.!KS.     i 

PLACKS,  AND  STEAM   IU  )l  I.E1JS.     1;. 

I.'..  A  KMSTItoXH,  C.  E.       1   vol.   ISnio,  boards. 

50  cents. 

No.  3.— STEAM    F.'.OILEI,'    EXPLOSIONS.     J!v   /i  - 
i:.\ll   ( .'or,  1:1  UN.      1  Nmo,  boards.     •">!' 

No.  ».— rEACTTCAL   DESIUNIXO    OF    I.ETAIN- 
IX<!  WALI-S.     ByAuTirm;  JACOB,  A.  I'., 

ISjiio,  boards.     .r>0  cents. 

No.  I.    i vn PORTIONS    OK     IMXS     rsi;i»    IN 

BIITDCES.      J'.y   (!|i\i;i,i:s    |',I.M)|  i;.  ( '.  I'.. 
.,  boards.       •")()  cents.      (IJeady  > 

X,,.  r,._\-ENTIL.\Ti  i\  OF  BUILDIN   tS.     • 

F.  I>1   ri.KIi.      ISnio,  boards.      ."io 

preparation-) 

No.  0. -ON  TH'K   I ) KS I ( :  N I X (I  A  N  I )  <  '<  »N ST RUC- 
TION  or  STOJ;AGE    i;i>;;i,\ oii;s. 

I'.y   AKTIIUK  .T.\co;;,  A.  ~\'>.      ifemo,  boards. 
5!>  cents.     (In  preparation.) 


tree  by  mail  on  receipt  o!'  price. 


